Four-Dimensional Mathematics Creates the Super Universe

In the common theory of the Universe, the redshift of the light wavelength from distant stars indicates the speed of the star. In this study, the model of the Universe is the surface volume of the four-dimensional sphere, and the shape of the Universe results in the most of the redshift of light wavelength. Therefore, there is no dark energy accelerating the Universe. The surface of the four-dimensional sphere is a volume, and this volume is a good model for the Universe. The surface volume of the four-dimensional sphere has been explained by a model of four-dimensional cube, within which the forming of surface volume can be easily shown. The model of four-dimensional cube containing six side cubes is ingenious for explaining the structure of the four-dimensional Universe, but it is not enough because the four-dimensional cube has not six side cubes, but eight side cubes. Therefore, in this study a better method has been created to construct the four-dimensional cube. Our three-dimensional Universe is the surface of the four-dimensional sphere Universe. The volume of our three-dimensional Universe is finite, and beneath it is the infinite volume four-dimensional Super Universe. Two important basic formulae have been derived: The surface volume of the four-dimensional sphere is π3R3 in which R is the radius of the sphere, and the fourth-power volume of the four-dimensional sphere is 1/4 π3R4. The volume of the Universe has been calculated π3R3 = 62 × 1030 ly3. Time as the fourth dimension of the space takes effect only near the speed of light, and therefore it has been ignored in this study.

Enhancing Learners’Performance in Grade 7 Mathematics Through 50-30-20 Exercise

Assessment exercises constitute a crucial component of the teaching and learning process,serving the purpose of gauging the degree to which learning objectives have been accomplished.This study aims to assess the mathematics performance of Grade 7 learners using the 50-30-20 exercise.Specifically,this study seeks to determine the learners’pre-test and post-test mean scores,identify significant differences between the pre-test and post-test results,evaluate learners’exercises,and propose enhanced exercises.The research employs a quasi-experimental design,with 40 Grade 7 learners in the school year 2023-2024 as participants,selected through purposive non-random sampling.Statistical data analysis involves the use of mean,standard deviation,paired t-test,and Cohen’s D effect size.Ethical considerations were paramount,as evidenced by a letter of authorization from the school head outlining the strict adherence to voluntary participation,informed parental consent,anonymity,confidentiality,risk mitigation,results-sharing protocols,and the commitment to keeping research data confidential.The data yielded a remarkable outcome:the experimental group exhibited improvement in both the pre-test and post-test.This result substantiates the initial objective of the study,showcasing a noteworthy and favorable performance among the participants.Consequently,it suggests that a majority of the participants strongly agree that the 50-30-20 exercises contribute to enhancing their understanding and problem-solving skills,as well as their ability to grasp mathematical concepts and improve their overall performance in mathematics.Therefore,the 50-30-20 exercises not only facilitated students in understanding mathematics lessons but were also aligned with the Department of Education’s development plan.

THREE-DIMENSIONAL MATHEMATICAL MODEL AND ITS APPLICATION IN THE NEIGHBORHOOD OF THE THREE GORGES RESERVOIR DAM IN THE YANGTZE RIVER

The calculation of flow and sediment transport is one of the most important tasks in river engineering. The task is particularly difficult because a number of complex physical phenomena should be accounted for more realistically in a model with a predictive power. Three-dimensional calculations of river flow and suspended sediment transport are performed in this paper with application in the Three Gorges Reservoir in the Yangtze River. A period of 76 years after the dam is built is simulated and the results are compared with laboratory measurements obtained by Tsinghua University whereby the model is verified and calibrated. Generally speaking, the calculated results agree well with the experiments, demonstrating that the present model can be used for flow and sediment transport prediction in rivers.

A two-dimensional mathematical model of a Zn-MnO_2 alkaline cell(1)

A two-dimensional mathematical model based on the macrohomogeneous theory of porous electrodes was developed for a cylindrical Zn-MnO2 alkaline cell. The model was applied to understand the effect of the length of the anode current collector on the cell performance. Results are presented for the continuous discharge at a high rate of 1A and a moderate rate of 0.2A for a AA-sized cell. With a typical length of an anode current collector at about 70%of the cell height, the analysis showed that an increase in the length of the anode current collector would benefit the lower rate of discharge more than the higher rate of discharge.

Analysis of three-dimensional vortexes below the free surface in a continuous casting mold

To study fluctuations of the free surface of liquid steel in the mold,two different models with the same casting conditions but different thicknesses were employed to analyze the hydrodynamic behavior at the top of the mold.The first model was a standard thickness slab,and the second had a thickness three times wider.It is found with the second model that above the plane formed by the steel jets,it is possible to observe four three-dimensional vortexes that interact with the submerged entry nozzle（SEN）and mold walls.By using a biphasic model to simulate the interface between the liquid and air inside the mold,the flow asymmetry and the fluctuations of the free surface can be clearly observed.

Three-Dimension Mathematical Model of Total Phosphor in the Reservoir and Application

Taking the transport of total phosphor pollutants in the Beijing Miyun reservoir for example,we have obtained three dimensional distributing regularity of total phosphor pollutants by the calculation of the linear interpolation value of each point between horizontal layers. The credibility analysis in allusion to this method was carried out and the programming scheme for realizing this method was set forth.

Numerical study on three-dimensional flow field of continuously rotating detonation in a toroidal chamber

Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonation- shock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interest- ing properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems.

Infinite Three-Dimensional Coordination Polymers: Synthesis and Structures of [Cd (4,4'-bpy)_2 (H_2O)_2]_n (pic)_(2n),[Zn (4,4'-bpy)_2 (H_2O)_2]_n(pic)_(2n) (H_2O)_(2n), and [Zn (4,4'-bpy)_2 (H_2O)_2]_n (4,4'-bpy)_n(H_2O)_n (pic)_(2n)

Three Complexes of the formula [Cd (4,4'-bpy)_2 (H_2O)_2]_n. (pic)_(2n) (1) [Zn (4,4'-bpy)_2 (H_2O)]_n (4,4'-bpy)_n(H_2O)_n (pic)-(2n) (2) and [Zn (4,4'-bpy)_2 (H_2O)]_n (4,4'-bpy)_n (pic)-(2n)(H_2O)_n (3) (4.4'-bpy = 4.4'-bipyridine. pic = picric anion ) have been synthesized and characterized by elemental analysis and single-crystal x-ray diffraction. They all have infinite three-dimensional network structure. crystallizing in the monoclinic space group C2/c (1) and Cc (2.3).

Three-dimensional tidal current numerical model of the Oujiang Estuary

The characteristics of three-dimensional （3-D） tidal current in the Oujiang Estuary are investigated according to in situ observations. The Oujiang Estuary has features of irregular coastline, complex topography, many islands, moveable boundary, and submerged dyke, therefore, σ 3-D numerical model oil an unstructured triangular grid has been degeloped. The σ coordinate transforination, the moveable boundary and submerged dyke treatment techniques were employed in the model so it is suitable for the tidal simulations in the Oujing Estuary with submerged dyke and moveable boundary problems. The model is evaluated with the in situ data, and the results show that the calculated water elevations at 19 stations and currents at 19 profiler stations are in good agreement with measured data both in magnitude and phase. This numerical model is applied to the 3-D tidal circulation simulations of experiments in stopping flow transport through the South Branch of the Oujiang Estuary, and the feasibility to cutoff the flow in the South Branch of the Oujiang Estuary is demonstrated by numerical simulation experiments. The developed numerical model simulated the 3-D tidal current circulations in complicated coastal and estuarine waters very well.

Three-Dimensional Water-Quality Simulation for River Based on VOF Method

In the present study, considering the transport and transformation processes of variables, a threedimensional water quality model for the river system was established, which coupled the volume of fluid(VOF) method with the k-ε turbulence mathematical model. Then, the water hydrodynamic characteristics and transport processes for BOD_5, NH_(3^-)N and TP were analyzed. The results showed that the water surface of convex bank was a little lower than that of concave bank due to the centrifugal force near the bend, and most concentrations were inferior to the type Ⅴ standard indexes of surface water environmental quality. The model validation indicated that the errors between the simulated and monitored values were comparatively small, satisfying the application demands and providing scientific basis and decision support for the restoration and protection of water quality.

3-Dimensional Body Measurement Technology

3 - dimensional body measurement technology, the basis of developing high technology in industry, accelerates digital development of aplparel industry. This paper briefly introduces the history of 3 - dimensional body measurement technology, and recounts the principle and primary structure of some types of 3 - dimensional automatic body measurement system. With this understanding, it discusses prospect of 3- dimensional CAD and virtual technology used in apparel industry.

Mathematical Model of Steady State Operation in Jet Pipe Electro-Hydraulic Servo Valve

Jet pipe electro-hydraulic servo valve is the heart of feedback control systems,and it is one of the mechatronic components used for precision flow control application.It consists of several precision and ddicate components.The performance of the jet pipe servo valve depends on many parameters.During the developmental stage,it is very difficult to ascertain the function parameters.The steady-state analysis of jet pipe electro-hydraulic servo valve has been made to simulate its fluid characteristics （flowin,flow-out,leakage flow,recovery or load pressure,etc.） by mathematical modeling.Theoretical model was conducted on various affecting parameters on the pressure,the main flow rate of fluid,or leakage flow through the receiver holes.The major parameters studied are jet pipe nozzle diameters,receiver hole diameters,angle between the two centre-lines of receiver hole,nozzle offset,and nozzle stand-of distance.In this paper the research is important to determine and optimize the structural parameters of jet pipe servo valve.Thus,equations of the pressure and flow characteristics are set up and the optimal structural parameters of jet pipe are established.

Parametric study on single shot peening by dimensional analysis method incorporated with finite element method

Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and re- sistance to corrosion fatigue, cracking, etc. Compressive re- sidual stress and dent profile are important factors to eval- uate the effectiveness of shot peening process. In this pa- per, the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated. Firstly, dimensionless relations of pro- cessing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were de- duced by dimensional analysis method. Secondly, the in- fluence of each dimensionless parameter on dimensionless variables was investigated by the finite element method. Fur- thermore, related empirical formulas were given for each di- mensionless parameter based on the simulation results. Fi- nally, comparison was made and good agreement was found between the simulation results and the empirical formula, which shows that a useful approach is provided in this pa- per for analyzing the influence of each individual parameter.

A Comparative Analysis of the New -3(-n) - 1 Remer Conjecture and a Proof of the 3n + 1 Collatz Conjecture

This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.

多维动态网络的密钥认证数学建模与仿真

多维动态网络在密钥认证过程中,若加密的密钥安全程度较低,则会被量子计算机解码,使传输的隐私数据出现泄露。为有效提升密钥的安全认证效果,提出量子攻击下多维动态网络密钥认证数学建模方法。方法建立用于多维动态网络的密钥认证模型,在建立的认证模型中,对网络中待传输数据实施冗余清洗,并使用高级加密标准(Advanced Encryption Standard,AES)算法生成密钥对待传输数据初次加密;添加一串噪声数据在加密数据中,并对其二次加密,进一步提升数据的抗量子攻击性能,建立多维动态网络的安全密钥传输模型,完成密钥的安全传输。根据解密方法结合密钥对数据安全解密,完成多维动态网络密钥的安全认证。实验结果表明,利用上述方法开展网络密钥认证时,加解密时间短,认证准确率在85%以上,且抗量子攻击能力强。

生态海堤多级平台消浪特性及越浪量计算

针对生态海堤多级平台消浪设计依据缺乏、人工经验设计效率低且难以最大限度发挥消浪效能的问题,通过构建耦合高精度水气界面捕捉算法的三维数学模型,开展了生态海堤多级平台消浪特性及越浪量计算研究,并基于多级堤身结构(平台宽度、平台高度、堤防高度)不同组合下的越浪规律,提出了生态海堤越浪量计算公式。结果表明:受多级平台逐级抬高影响,堤身上覆水厚度变小造成波浪逐层浅化发生连续破碎耗能,同时多级平台迎水面分级阻挡浅化波传播,造成波浪逐级反射衰减;多级平台宽度和高度共同控制着堤顶越浪,越浪量相同情况下迎水面横向堤身宽度与纵向堤身高度变化值存在定量互换关系。

一种基于谱域-空域组合特征支持向量机的高光谱图像分类算法

针对高光谱图像分类问题,提出了一种基于支持向量机的利用组合特征对高光谱图像进行分类的算法,组合特征综合了高光谱图像的光谱域和空域信息。针对图像的高维数据特性,利用最大噪声分量方法进行特征提取,对得到的主分量图像,采用虚拟维数估计算法来确定需要保留的主分量数目,并用数学形态学操作用保留的主分量图像中提取目标的形态信息。根据得到的空域特征并结合原始光谱域特征,构造用于分类的组合特征矢量。而且采用了支持向量机,利用了其支持小样本、效率高的优点。高光谱数据实验表明,本文提出的方法和单独使用谱域或空域信息进行分类相比,具有一定的优越性。

模糊C-均值聚类法在医学图像分析中的应用

主要针对医学图像提出了基于模糊均值聚类的改进算法和应用 .该方法分为 3步 ,第 1步是像素的模糊化 ,通过模糊期望值构造冗余图像 ;第 2步是通过冗余图像和原始图像进行聚类分割 ;第 3步是三维显示 .由于利用冗余图像增加了每个像素的特征量 ,该算法增强了聚类分割的精确度 .同时 ,还给出了应用自行开发的三维医学图像处理与分析系统对多种医学图像 (包括 CT、螺旋 CT和 MRI)的处理结果 .由于对薄骨和关节接合处骨骼的较好识别 ,使其重建后的三维模型可以清晰地再现解剖结构 。

倒立摆的一种FUZZY-PD复合控制器设计

针对高维模糊控制器设计中的"规则爆炸"问题,以倒立摆为研究对象,直接将四维控制器分解为两个二维控制器,其中一个为PD控制器、一个为二维模糊控制器,并将这两个控制器输出直接叠加作为控制量.在此基础上,借助状态反馈极点配置方法,提出了一种比较系统化的模糊控制器参数估计方法,以弥补模糊控制器参数系统化设计方法的不足.对倒立摆系统的仿真及对它的实时控制结果均验证了该复合控制方案及这种模糊控制器参数估计方法的有效性.